{"id":7820,"date":"2020-02-02T23:49:01","date_gmt":"2020-02-03T04:49:01","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/matg1003\/?p=7820"},"modified":"2020-02-02T23:49:01","modified_gmt":"2020-02-03T04:49:01","slug":"2019-2020-termino-2-e2-tema-4","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/matg1049\/2019-2020-termino-2-e2-tema-4\/","title":{"rendered":"Tema 4"},"content":{"rendered":"<div class='dropshadowboxes-container ' style='width:auto;'>\r\n                            <div class='dropshadowboxes-drop-shadow dropshadowboxes-rounded-corners dropshadowboxes-inside-and-outside-shadow dropshadowboxes-lifted-bottom-left dropshadowboxes-effect-default' style=' border: 1px solid #dddddd; height:; background-color:#ffffff;    '>\r\n                            Examen | 2019-2020 | T\u00e9rmino 2 | Segunda Evaluaci\u00f3n | Tema 4\r\n                            <\/div>\r\n                        <\/div>\n<hr \/>\n<p style=\"text-align: justify\">A continuaci\u00f3n, se presentan dos enunciados que son verdaderos, escoja uno de ellos y demu\u00e9strelo.<\/p>\n<table style=\"border: none\">\n<tbody>\n<tr>\n<td style=\"text-align: justify;border: none\" width=\"6%\">a)<\/td>\n<td style=\"text-align: justify;border: none\" width=\"94%\">Sean <span class=\"wp-katex-eq\" data-display=\"false\">V<\/span> y <span class=\"wp-katex-eq\" data-display=\"false\">W<\/span> dos espacios vectoriales ambos sobre un mismo campo <span class=\"wp-katex-eq\" data-display=\"false\">\\mathbb{K}<\/span>. Suponga que <span class=\"wp-katex-eq\" data-display=\"false\">V<\/span> es de dimensi\u00f3n finita y <span class=\"wp-katex-eq\" data-display=\"false\">B=\\{ v_1,v_2,...,v_n\\}<\/span> es una base de <span class=\"wp-katex-eq\" data-display=\"false\">V<\/span> y <span class=\"wp-katex-eq\" data-display=\"false\">w_1,w_2, ..., w_n<\/span> son vectores en <span class=\"wp-katex-eq\" data-display=\"false\">W<\/span>, entonces existe una transformaci\u00f3n lineal <span class=\"wp-katex-eq\" data-display=\"false\">T:V\\longrightarrow W<\/span> tal que <span class=\"wp-katex-eq\" data-display=\"false\">T(v_i)=w_i<\/span> para cada <span class=\"wp-katex-eq\" data-display=\"false\">i=1,2,...,n<\/span>.<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: justify;border: none\">b)<\/td>\n<td style=\"text-align: justify;border: none\">Sea <span class=\"wp-katex-eq\" data-display=\"false\">(V,\\langle \\cdot | \\cdot \\rangle)<\/span> un espacio vectorial con producto interno y sea <span class=\"wp-katex-eq\" data-display=\"false\">W<\/span> el espacio generado por el conjunto ortonormal de vectores <span class=\"wp-katex-eq\" data-display=\"false\">\\{ v_1,v_2,...,v_n \\}<\/span>. El vector <span class=\"wp-katex-eq\" data-display=\"false\">v\\in V<\/span> pertenece a <span class=\"wp-katex-eq\" data-display=\"false\">W<\/span> si, y s\u00f3lo si, <span class=\"wp-katex-eq\" data-display=\"false\">u<\/span> puede ser escribirse como <span class=\"wp-katex-eq\" data-display=\"false\">\\langle u | v_1 \\rangle v_1+\\langle u | v_2 \\rangle v_2 + ... + \\langle u | v_n \\rangle v_n<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>A continuaci\u00f3n, se presentan dos enunciados que son verdaderos, escoja uno de ellos y demu\u00e9strelo. a) Sean y dos espacios vectoriales ambos sobre un mismo campo . Suponga que es de dimensi\u00f3n finita y es una base de y son vectores en , entonces existe una transformaci\u00f3n lineal tal que para cada . b) Sea &hellip; <a href=\"https:\/\/blog.espol.edu.ec\/matg1049\/2019-2020-termino-2-e2-tema-4\/\" class=\"more-link\">Sigue leyendo <span class=\"screen-reader-text\">Tema 4<\/span><\/a><\/p>\n","protected":false},"author":609,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[1430169],"tags":[],"class_list":["post-7820","post","type-post","status-publish","format-standard","hentry","category-segunda-evaluacion-termino-2-2019-2020"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/posts\/7820","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/users\/609"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/comments?post=7820"}],"version-history":[{"count":0,"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/posts\/7820\/revisions"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/media?parent=7820"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/categories?post=7820"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/matg1049\/wp-json\/wp\/v2\/tags?post=7820"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}